Droop-Controlled Inverters in Microgrids are Kuramoto Oscillators ?

Motivated by the recent interest in smart grid technology and by the push towards distributed and renewable energy, we study the parallel operation of DC/AC inverters in a lossless microgrid. We show that the parallel interconnection of DC/AC inverters equipped with conventional droop controllers is precisely described by the Kuramoto model of coupled phase oscillators. This novel description, together with results from the theory of coupled oscillators, allows us to characterize the behavior of the network of inverters. Specifically, we provide a necessary and sufficient condition for the existence of a equilibrium point that is unique, stable and almost globally attractive. Remarkably, our condition is independent of the overall scaling on the collection of droop coefficients. Moreover, we present a simple and new derivation of the well-known coefficient matching condition for proportional power sharing among inverters. These results hold without assumptions on identical line characteristics or voltage magnitudes.